This invention relates to a method for determining preselected performance characteristics of the tread of a tyre, comprising ride comfort, noise and handling, and to a tyre provided with a tread having optimal characteristics with reference to said performance characteristics.
The subject of this inventions a method which allows to determine a set of performance characteristics of the tread of a tyre by means of a single criterion which refers to all the performance characteristics taken into account.
An initial aspect of the invention is a method for determining preselected performance characteristics of the tread of a tyrexe2x80x94comprising ride comfort, noise and handlingxe2x80x94where a longitudinal direction (x), a transversal direction (y) and a vertical direction (z) are associated with said tread, where said tread has a preselected thickness and a preselected circumferential development and is made from a preselected rubber compound and comprises blocks and grooves having at least a preselected pitch, each portion of said tread in contact with a road surface having a contact area, said method comprising the following phases:
a) dividing said tread into a 3-D grid of full cells and empty cells of preselected dimensions (dxdydz);
b) identifying piles of said cells in said grid, each pile of cells having a base area equal to that of one cell (dxdy) and a height equal to said thickness of the tread, said piles of cells being full, empty or partially full;
c) identifying a group of said piles of cells present under a contact area;
d) determining a stiffness value in the longitudinal direction cxj and a stiffness value in the transversal direction cyj for each pile of cells in said contact area;
e) identifying families of discrete areas in said contact area, each discrete area of each family having preselected dimensions in said longitudinal direction (x) and in said transversal direction (y);
f) dividing said contact area in transversal strips with a preselected length in said longitudinal direction (x), each transversal strip comprising a set of said piles of cells;
g) determining a stiffness value per unit of length in the longitudinal direction cpx and a stiffness value per unit of length in the transversal direction cpy for each of said transversal strips (30), by summing said stiffness values in the longitudinal direction cxj and said stiffness values in the transversal direction cyj of said piles of cells of said set, respectively;
h) assigning a preselected deformation state to each of said transversal strips;
i) determining at least one force per unit of length associated with each transversal strip by means of a preselected function linking one of said stiffness values cpx and cpy and said deformation state
j) summing preselected forces per unit of length of all the transversal strips associated with a discrete area to attain at least one preselected single force acting in one of said longitudinal (x) and transversal (y) directions;
k) determining at least one total force associated with said contact area by means of a suitable summation of preselected single forces associated with all the discrete areas of said contact area, said total force being representative of at least one of said performance characteristics;
l) repeating the steps from c) to k) for all the portions of said tread which are arranged in succession on said circumferential development and come in contact with said road surface in an entire revolution of said tyre by means of respective contact areas to attain a plurality of total forces associated with all the contact areas of said tread and
m) evaluating the pattern of said plurality of total forces to establish whether the arrangement of said full cells and empty cells in said 3-D grid is substantially uniform along said circumferential development and generates total forces with substantially equal and constant values, so as to optimize at least one preselected performance characteristic of said tread.
Preferably said stiffness values cxj and cyj are given by the following relationships:
cxj=xcex7xGAp/h
cyj=xcex7yGAp/h
where G is a preselected value for the modulus of elasticity in shear of said compound, Ap is the area of said pile of cells, h is said height of said pile of cells, xcex7x is a coefficient of efficiency in said longitudinal direction (x) and xcex7y is a coefficient of efficiency in said transversal direction (y), where said coefficients of efficiency xcex7x and xcex7y depend on the respective slenderness ratios xcexjx and xcexjyxe2x80x94which, in turn, respectively depend on the ratio between the length of said pile of cells (dx) in said longitudinal direction and the height of said pile of cells and between the width of said pile of cells (dy) in said transversal direction and the height of said pile of cellsxe2x80x94and on a shape coefficient which is a function of the position of said pile of cells in said grid.
Advantageously, each aforesaid discrete area has a length in said longitudinal direction (x) which is equal to said pitch of said tread.
Preferably, said length of each transversal strip is equal to a unit of length of said stiffness values cpx and cpy.
According to a preferred embodiment, in the aforesaid phases from i) to l), total longitudinal forces are determined by means of said stiffness values per unit of length in the longitudinal direction cpx of said strips and by means of a triangular longitudinal shearing deformation state of said tread, where said longitudinal deformation is null at the start of the contact area and maximum at the end of the contact area.
According to another preferred embodiment, in the aforesaid phases from i) to l), total transversal forces are determined by means of said stiffness values per unit of length in the transversal direction cpy of said strips and by means of a triangular transversal shearing deformation state of said tread, where the transversal deformation is null at the start of the contact area and maximum at the end of the contact area.
Preferably, total longitudinal stiffness values Kx associated with said contact areas of said tread are determined. Total transversal stiffness values Ky associated with said contact areas of said tread are also determined.
According to an additional preferred embodiment, total torsional stiffness values Kt associated with said contact areas of said tread are determined by means of the following phases:
n) identifying plane elements (dxdy) of said piles of cells under said contact area;
o) imposing a rotation on said contact area with respect to its centre of gravity;
p) determining the slip of each plane element (dxdy) in said contact area;
q) splitting said slip into a longitudinal component and a transversal component;
r) multiplying said longitudinal slip component by said longitudinal stiffness cxj and said transversal slip component by said transversal stiffness cyj to obtain elementary forces which, multiplied by the offset of said plane element (dxdy) with respect to said centre of gravity generate torque values and
s) summing said torque values to obtain a total torsional moment which, linked with said rotation, results in said total torsional stiffness Kt for each contact area.
Preferably, said stiffness values Kx, Ky and Kt have the following values:
Kx=2,300-2,500 N/mm
Ky=2,400xe2x80x942,600 N/mm
Kt=80-88 N*m/degree
Preferably, the ratio between said stiffness values Ky and Kx has the following values:
Ky/Kx=0.98-1.05.
Advantageously, said piles of cells in said 3-D grid form a histogram in which a preselected character is associated with each pile of cells, said histogram being included in an optimal field delimited by a preselected lower surface and by a preselected upper surface.
Preferably, said histogram optimizes said total longitudinal stiffness values Kx, making said total longitudinal forces assume a mean value which is lower than a preselected limit to thus minimize the noise output by said tread and optimizing ride comfort.
Advantageously, said histogram also maximizes said total transversal stiffness values Ky, making said total transversal forces assume values which are higher than a preselected limit to thus optimize said tread with reference to handling.
Additionally, said histogram maximizes the total torsional stiffness values Kt in said contact areas, making the total torsional moments of said contact areas assume values which are higher than a preselected limit to thus optimize said tread with reference to handling.
A second aspect of this invention relates to a tyre provided with a tread having optimal characteristics with reference to preselected performance characteristics, comprising ride comfort, noise and handling, where a longitudinal direction (x), a transversal direction (y) and a vertical direction (z) are associated with said tread, where said tread has a preselected thickness and a preselected circumferential development and is made from a preselected rubber compound and comprises blocks and grooves having at least a preselected pitch, each portion of said tread in contact with a road surface having a contact area, where said tread is divisible into a 3-D grid of full cells and empty cells of preselected dimensions, where in said grid piles of said cells are identified, each pile of cells having a base area equal to that of one cell (dxdy) and height equal to said thickness of the tread, said piles of cells being full, empty or partially full, a group of said piles of cells being identifiable under each contact area, each pile of cells having a stiffness value in the longitudinal direction cxj and a stiffness value in the transversal direction cyj, where discrete areas with a preselected length in said longitudinal direction (x) and a preselected width in said transversal direction (y) are identifiable in said contact area, said contact area being divisible into transversal strips with a preselected length in said longitudinal direction (x), each transversal strip comprising a set of said piles of cells and having a stiffness value per unit of length in the longitudinal direction cpx and a stiffness value per unit of length in the transversal direction cpy determined by the summation, respectively, of said stiffness values in the longitudinal direction cxj and said stiffness values in the transversal direction cyj of said piles of cells in said set, at least one force per unit of length being associated with each transversal strip which depends on one of the said stiffness values per unit of length cpx and cpy and on a preselected state of deformation of said transversal strip, where at least one single force consisting of the sum of preselected forces per unit of length of all the transversal strips of said discrete area is associated with each discrete area, where a total force consisting of the sum of preselected single forces of all the discrete areas of said contact area are associated with each contact area, where said total force is representative of at least one of said performance characteristics, where said full and empty cells have a substantially uniform arrangement along said circumferential development of said tread and generate total forces associated with all the contact areas of all the portions of said tread in contact during one entire revolution, having values substantially equal and constant so as to optimize at least one preselected performance characteristic of said tread.
Preferably, said stiffness values cxj and cyj depend on preselected parameters of said tyre, according to the relationships given above.
Preferably, each discrete area and each transversal strip has a length equal to the aforementioned values.
Advantageously, a total longitudinal force and a total transversal force are associated with each contact area.
Preferably, a total longitudinal stiffness value Kx and a total transversal stiffness value Kyxe2x80x94as well as a total torsional stiffness value Ktxe2x80x94are associated with each contact area.
Preferably, the aforesaid stiffness values Kx, Ky and Kt have the aforementioned values and the ratio between the aforesaid stiffness values Kx and Ky has the aforementioned values.
Advantageously, said piles of cells in said 3-D grid form a histogram with the aforementioned properties.
According to a preferred embodiment, said tread has a central longitudinal groove, a first, a second and a third lateral longitudinal groove (on the left and on the right), transversal grooves and portions of transversal grooves (on the left and on the right) connected by portions of longitudinal grooves. Said central longitudinal groove and each first lateral longitudinal groove delimit a rib. Each first and second lateral longitudinal groove and said transversal grooves delimit a central internal row of first blocks. Each second and third lateral longitudinal groove, said transversal grooves and said portions of transversal grooves delimit a central external row of second blocks. Each third longitudinal groove, said portions of longitudinal grooves, said transversal grooves and said portions of transversal grooves delimit a shoulder row of third and fourth blocks. Each of said first blocks has a transversal sipe and each of said second blocks has two transversal sipes.
Preferably, said tread hasxe2x80x94with a modulus of elasticity in shear G equal to 1xe2x80x94the following stiffness values Kx, Ky and Kt:
Kx=2345 N/mm
Ky=2412 N/mm
Kt=81 N*m/degree.
Advantageously, said tread hasxe2x80x94for a modulus of elasticity in shearing G equal to 1xe2x80x94the following ratio between stiffness values Ky and Kx:
Ky/Kx=1.03.
A third aspect of this invention relates to a tyre provided with a tread having optimal characteristics with reference preselected performance characteristics, comprising ride comfort, noise and handling, where a longitudinal direction (x), a transversal direction (y) and a vertical direction (z) are associated with said tread, where said tread has a preselected thickness and a preselected circumferential development and is made from a preselected rubber compound and comprises blocks and grooves having at least a preselected pitch, each portion of said tread in contact with a road surface having a contact area, where a total longitudinal stiffness value Kx, a total transversal stiffness value Ky and a total torsional stiffness value Kt are associated with each contact area, said stiffness values Kx, Ky and Kt having the following values:
Kx=2,300-2,500 N/mm
Ky=2,400-2,600 N/mm
Kt=80-88 N*m/degree.
Preferably, the ratio between said stiffness values Ky and Kx has the following values:
Ky/Kx=0.98-1.05.
In particular, said tread hasxe2x80x94for a modulus of elasticity in shear G equal to 1xe2x80x94the following stiffness values Kx, Ky and Kt:
Kx=2345 N/mm
Ky=2412 N/mm
Kt=81 N*m/degree.
Furthermore, said tread hasxe2x80x94for a modulus of elasticity in shear G equal to 1xe2x80x94the following ratio between stiffness values Ky and Kx:
Ky/Kx=1.03.
The method and the tyre according to this invention are based on a xe2x80x9cfull and emptyxe2x80x9d evaluation criterion (full cells and empty cells) in discrete areas of the tread in the contact area. The empty and full elements allow to identify several typologies of discrete areas in the tread pattern (as families of blocks or parts of blocks) and for each typology or family of discrete areas the stiffness can be estimated by means of preselected equations, known to construction engineers. The contact area consists of a suitable set of discrete areas and the stiffness of each discrete area contributes to the total stiffness of the portion of tread in the contact area in the longitudinal direction Kx, transversal (lateral) direction Ky and torsional sense Kt. This is because the contact area is divided into transversal strips of a preselected length in the longitudinal direction (x). Each strip comprises a set of piles of cells with a stiffness value in the longitudinal direction cxj and a stiffness value in the transversal direction cyj. The stiffness per unit of length in the longitudinal direction cpx and the stiffness per unit of length in the transversal direction cpy of each strip result respectively from summing the values of cxj and the values of cyj of the piles of cells of the set. The sum of the stiffness values per unit of length cpx and the sum of the stiffness values per unit of length cpy relative to the transversal strips form the longitudinal stiffness Kx and the transversal stiffness Ky of the tread, respectively. The cpx values are summed to obtain Kx and the cpy values are summed to obtain Ky.
Consequently, given the longitudinal stiffness per unit of length cpx of each discrete area, the corresponding longitudinal force per unit of length can be computed by assigning a specific deformation state and, consequently, so can the force relating to a discrete area. When the length of each discrete area is equal to a single pitch, the force is called xe2x80x9cbasic curvexe2x80x9d.
The total longitudinal force (shearing or slipping force) under the contact area is determined as the sum of the longitudinal forces per unit of length of the contact area, by subjecting the contact area to a triangular shearing deformation statexe2x80x94i.e. a deformation which is null at the start of the contact area and maximum at the endxe2x80x94and by using a brush model (known to a person skilled in the art) separated in the longitudinal direction.
The total longitudinal force value is relating to a position of the contact area with respect to the entire development of the tread. The calculation of the total longitudinal force is repeated for several positions of the contact area so as to attain the force pattern for an entire tyre revolution and estimate its mean value and its variation (oscillation) around this value.
The ride comfort and the noise output by the treadxe2x80x94in particular the output xe2x80x9csignal volumexe2x80x9dxe2x80x94are optimized by controlling the longitudinal force.
The expression xe2x80x9csignal volumexe2x80x9d is herein used to indicate the intensity of the noise output by the tread, i.e. the absolute noise volume.
The ride comfort is optimized by minimizing the longitudinal force generated by the tread during tyre rolling on any type of road surface (consequently, including irregular road surfaces and/or isolated obstacles, i.e. manhole covers, tram tracks, etc.). In particular, the harmonic components of the longitudinal forcexe2x80x94involving frequencies between 0 and 150 Hzxe2x80x94are considered.
In turn, the noise output by the tread when rolling is minimized by means of an optimal pattern of longitudinal stiffness per unit of length of the tread in its circumferential development, i.e. by means of a longitudinal force with a low mean value and limited oscillations around this value. This allows to reduce the xe2x80x9cvolumexe2x80x9d of the output noise (with equal modulus of elasticity G of the tread compound). In this case, the harmonic components of the longitudinal force involve frequencies exceeding 150 Hz.
The noise output by the tyre when cornering, i.e. in conditions involving leaning and vertical load transfer, is minimized by taking into account the variations in length of the contact area with the vertical load. In other words, both the variations of the contact area along the circumferential development and the variations in the contact area due to rapid variations of the vertical load are taken into account.
The method according to this invention also allows to determine the slip angle (force) of the tread of a tyre when cornering by means of the stiffness per unit of length cpy in the transversal direction. Also in this case, a brush model is used and a triangular transversal (shearing) deformation is imposed on the contact area, i.e. a deformation which is null at the start of the contact area and maximum at the end of the contact area. The transversal stiffness of the tread Ky resultsxe2x80x94as mentioned abovexe2x80x94from the sum of the stiffness values per unit of length cpy relative to the transversal strips which the contact area is divided into.
Handling is optimizedxe2x80x94as far as the contribution of the tread to the slip angle is concernedxe2x80x94by means of a high transversal stiffness of the tread involved in the contact. This is obtained by controlling the stiffness per unit of length in the transversal direction of the tread.
The method according to this invention also allows to determine the torsional stiffness of the tread using the stiffness values of the piles of cells in the longitudinal direction cxj and in the transversal direction cyj. The total torque Ckt generated by a revolution imposed on the contact area is determined: the ratio between the torque and the revolution is the total torsional stiffness Kt of the tread under contact.
A high torsional stiffness of the tread allows to additionally optimize handling. This is attained by controlling the stiffness values per unit of length in the longitudinal and lateral direction and the geometrical position of these stiffness values (i.e. of the cell of the tread to which these stiffness values refer) in the contact area.
Consequently, the typology of full and empty elements allows to control the variation of longitudinal, transversal and torsional stiffness during tyre rolling. These variations of stiffness influence the performance of the tyre with respect to a vehicle (vibrations, handling) and the external environment (vibrations, noise).